We have customers who have iPhones and require shared contacts once they move to Microsoft Office 365: can CiraSync support this functionality?

Yes, CiraSync can sync Office 365 contacts to iPhones. Once your customers move to Office 365, CiraSync will sync contacts and calendars from the GAL, Public Folders, and shared mailboxes to Office 365 mailboxes and then propagate the sync to iPhones through the native exchange connector.